"... In PAGE 5: ... In addition, the measures of purity and entropy are easily derived from the confusion matrix[6]. Table2 summarizes the results of applying Algorithm Bi- partition to the MedCran data set. The confusion matrix at the top of the table shows that the document cluster D0 consists entirely of the Medline collection, while 1400 of the 1407 documents in D1 are from Cranfield.... In PAGE 5: ... The confusion matrix at the top of the table shows that the document cluster D0 consists entirely of the Medline collection, while 1400 of the 1407 documents in D1 are from Cranfield. The bottom of Table2 displays the top 7 words in each of the word clus- ters W0 and W1. The top words are those whose internal edge weights are the greatest.... ..."

"... In PAGE 14: ... Table1 presents some important member functions used in the initialization and simulation of a CSP model. We discuss some of these function in detail here.... In PAGE 14: ...imulation of the CSP model starts by calling the sc csp start(...) function. Table1 shows a list of some important functions and variables and whether the CSP kernel or the QuickThread package manages them [6, 9]. The variable m cor pkg is a pointer to the file static instance of the coroutine package.... ..."

"... In PAGE 5: ...54 they were evaluated. Table3 shows contribution values grouped by the different instance types. They are retrieved by first calculating the success rate of each neighborhood structure and then scaling these values s.... ..."

"... In PAGE 9: ... An element of intra-generational redistribution was maintained, but in the form of a minimum top-up, means-tested pension benefit financed outside the pension system. As summarized in Table4 , workers deciding to stay in the reformed PAYG will pay a contribution rate of 30 percent of their gross wages, and will earn an accrual rate of 1.65 percent for each year of service.... ..."

"... In PAGE 8: ...38 -100 No No Next we evaluated each cluster for a threshold separately. The results for the CRAN collection are shown in Table6 . Similar results were obtained for MED and CISI.... ..."

"... In PAGE 5: ... Finally, these codes have been used as a platform for the implementation of the uniprocessor version of Level 3 BLAS on the BBN TC2000 (see next Section). We show in Table1 the MFlops rates of the parallel matrix-matrix multiplication, and in Table 2 the performance of the LU factorization (we use a blocked code similar to the LAPACK one) on the ALLIANT FX/80, the CRAY-2, and the IBM 3090-600J obtained using our parallel version of the Level 3 BLAS. Note that our parallel Level 3 BLAS uses the serial manufacturer-supplied versions of GEMM on all the computers.... In PAGE 6: ... This package is available without payment and will be sent to anyone who is interested. We show in Table1 the performance of the single and double precision GEMM on di erent numbers of processors. Table 2 shows the performance of the LAPACK codes corresponding to the blocked LU factorization (GETRF, right-looking variant), and the blocked Cholesky factorization (POTRF, top-looking variant).... In PAGE 8: ... The second part concerned the performance we obtained with tuning and parallelizing these codes, and by introducing library kernels. We give in Table1 a brief summary of the results we have obtained: One of the most important points to mention here is the great impact of the use of basic linear algebra kernels (Level 3 BLAS) and the LAPACK library. The conclusion involves recommendations for a methodology for both porting and developing codes on parallel computers, performance analysis of the target computers, and some comments relating to the numerical algorithms encountered.... In PAGE 12: ... Because of the depth rst search order, the contribution blocks required to build a new frontal matrix are always at the top of the stack. The minimum size of the LU area (see column 5 of Table1 ) is computed during during the symbolic factorization step. The comparison between columns 4 and 5 of Table 1 shows that the size of the LU area is only slightly larger than the space required to store the LU factors.... In PAGE 12: ... The minimum size of the LU area (see column 5 of Table 1) is computed during during the symbolic factorization step. The comparison between columns 4 and 5 of Table1 shows that the size of the LU area is only slightly larger than the space required to store the LU factors. Frontal matrices are stored in a part of the global working space that will be referred to as the additional space.... In PAGE 12: ... In a uniprocessor environment, only one active frontal matrix need be stored at a time. Therefore, the minimum real space (see column 7 of Table1 ) to run the numerical factorization is the sum of the LU area, the space to store the largest frontal matrix and the space to store the original matrix. Matrix Order Nb of nonzeros in Min.... In PAGE 13: ... In this case the size of the LU area can be increased using a user-selectable parameter. On our largest matrix (BBMAT), by increasing the space required to run the factorization (see column 7 in Table1 ) by less than 15 percent from the minimum, we could handle the ll-in due to numerical pivoting and run e ciently in a multiprocessor environment. We reached 1149 M ops during numerical factorization with a speed-up of 4.... In PAGE 14: ...ack after computation. Interleaving and cachability are also used for all shared data. Note that, to prevent cache inconsistency problems, cache ush instructions must be inserted in the code. We show, in Table1 , timings obtained for the numerical factorization of a medium- size (3948 3948) sparse matrix from the Harwell-Boeing set [3]. The minimum degree ordering is used during analysis.... In PAGE 14: ... -in rows (1) we exploit only parallelism from the tree; -in rows (2) we combine the two levels of parallelism. As expected, we rst notice, in Table1 , that version 1 is much faster than version 2... In PAGE 15: ... Results obtained on version 3 clearly illustrate the gain coming from the modi cations of the code both in terms of speed-up and performance. Furthermore, when only parallelism from the elimination tree is used (see rows (1) in Table1 ) all frontal matrices can be allocated in the private area of memory. Most operations are then performed from the private memory and we obtain speedups comparable to those obtained on shared memory computers with the same number of processors [1].... In PAGE 15: ... Most operations are then performed from the private memory and we obtain speedups comparable to those obtained on shared memory computers with the same number of processors [1]. We nally notice, in Table1 , that although the second level of parallelism nicely supplements that from the elimination tree it does not provide all the parallelism that could be expected [1]. The second level of parallelism can even introduce a small speed down on a small number of processors as shown in column 3 of Table 1.... In PAGE 15: ... We nally notice, in Table 1, that although the second level of parallelism nicely supplements that from the elimination tree it does not provide all the parallelism that could be expected [1]. The second level of parallelism can even introduce a small speed down on a small number of processors as shown in column 3 of Table1 . The main reason is that frontal matrices must be allocated in the shared area when the second level of parallelism is enabled.... In PAGE 17: ...5 28.2 Table1 : Results in Mega ops on parallel computers. In Table 1, it can be seen that the performance of the program on the Alliant FX/80 in double precision is better than the performance of the single precision ver- sion.... In PAGE 17: ...2 Table 1: Results in Mega ops on parallel computers. In Table1 , it can be seen that the performance of the program on the Alliant FX/80 in double precision is better than the performance of the single precision ver- sion. The reason for this is that the single precision mathematical library routines are less optimized.... In PAGE 18: ... block diagonal) preconditioner appears to be very suitable and is superior to the Arnoldi-Chebyshev method. Table1 shows the results of the computation on an Alliant FX/80 of the eight eigenpairs with largest real parts of a random sparse matrix of order 1000. The nonzero o -diagonal and the full diagonal entries are in the range [-1,+1] and [0,20] respectively.... In PAGE 19: ... A comparison with the block preconditioned conjugate gradient is presently being investigated.In Table1 , we compare three partitioning strategies of the number of right-hand sides for solving the system of equations M?1AX = M?1B, where A is the ma- trix BCSSTK27 from Harwell-Boeing collection, B is a rectangular matrix with 16 columns, and M is the ILU(0) preconditioner. Method 1 2 3 1 block.... In PAGE 26: ...111 2000 lapack code 0.559 Table1 : Results on matrices of bandwith 9.... In PAGE 30: ... We call \global approach quot; the use of a direct solver on the entire linear system at each outer iteration, and we want to compare it with the use of our mixed solver, in the case of a simple splitting into 2 subdomains. We show the timings (in seconds) in Table1 on 1 processor and in Table 2 on 2 processors, for the following operations : construction amp; assembly : Construction and Assembly, 14% of the elapsed time, factorization : Local Factorization (Dirichlet+Neumann), 23%, substitution/pcg : Iterations of the PCG on Schur complement, 55%, total time The same code is used for the global direct solver and the local direct solvers, which takes advantage of the block-tridiagonal structure due to the privileged direction. Moreover, there has been no special e ort for parallelizing the mono-domain approach.... ..."